Critical exponents of planar gradient percolation



The Annals of Probability

Critical exponents of planar gradient percolation

Pierre Nolin

Source: Ann. Probab. Volume 36, Number 5 (2008), 1748-1776.

Abstract

We study gradient percolation for site percolation on the triangular lattice. This is a percolation model where the percolation probability depends linearly on the location of the site. We prove the results predicted by physicists for this model. More precisely, we describe the fluctuations of the interfaces around their (straight) scaling limits, and the expected and typical lengths of these interfaces. These results build on the recent results for critical percolation on this lattice by Smirnov, Lawler, Schramm and Werner, and on the scaling ideas developed by Kesten.

Primary Subjects: 60K35, 82B43, 82B27
Keywords: Inhomogeneous percolation; gradient percolation; critical exponents; random interface

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Permanent link to this document: http://projecteuclid.org/euclid.aop/1221138765
Digital Object Identifier: doi:10.1214/07-AOP375
Mathematical Reviews number (MathSciNet): MR2440922

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